Related papers: How to Compute a Moving Sum
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
Interactive high-performance computing is doubtlessly beneficial for many computational science and engineering applications whenever simulation results should be visually processed in real time, i.e. during the computation process.…
The sliding window approach provides an elegant way to handle contexts of sizes larger than the Transformer's input window, for tasks like language modeling. Here we extend this approach to the sequence-to-sequence task of document parsing.…
Sums of the form $\sum_{N_m=q}^{n}{\cdots \sum_{N_1=q}^{N_2}{a_{(m);N_m}\cdots a_{(1);N_1}}}$ where the $a_{(k);N_k}$'s are same or distinct sequences appear quite often in mathematics. We will refer to them as recurrent sums. In this…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
We present GraSSP, a novel approach to perform automated parallelization relying on recent advances in formal verification and synthesis. GraSSP augments an existing sequential program with an additional functionality to decompose data…
The availability of large number of processing nodes in a parallel and distributed computing environment enables sophisticated real time processing over high speed data streams, as required by many emerging applications. Sliding window…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
These lecture notes are designed to accompany an imaginary, virtual, undergraduate, one or two semester course on fundamentals of Parallel Computing as well as to serve as background and reference for graduate courses on High-Performance…
We extend the known tables of pseudosquares and pseudocubes, discuss the implications of these new data on the conjectured distribution of pseudosquares and pseudocubes, and present the details of the algorithm used to do this work. Our…
This paper shows that the basic logic induced by the parallel recurrence of Computability Logic is a proper superset of the basic logic induced by the branching recurrence. The latter is known to be precisely captured by the cirquent…
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
High order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary order in a sliding window for data…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…